In the bipartite case, typically adopted measures are entropies, Schmidt rank, concurrence or entanglement of formation/distillation [1]}, [2]}. In the multipartite case, however, even more possibilities arise, reflecting the complexity of multipartite LOCC classification and the lack of a unique maximally entangled state [3]}, [4]}. These measures are often operationally related to communication tasks, where entanglement is seen as a resource for transcending the limitations of LOCC for distant parties. For many-body systems, however, other features are typically more relevant.
One measure that is important in this context is the best separable approximation (BSA) [5]}, [6]}, which captures to what extent the state \(\rho \)  of a many-body system can be approximated by a separable quantum state. Formally, the \(\mathcal {E}_{\text{BSA}}\)  is defined as the minimum real number \(t\in [0,1]\)  such that \(\rho \)  can be decomposed as
\(\rho = (1-t) \,\sigma + t\, \delta \rho \;,\) 
